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<div class="title">CompleteOrthogonalDecomposition.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2016 Rasmus Munk Larsen &lt;rmlarsen@google.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">struct </span>traits&lt;CompleteOrthogonalDecomposition&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    : traits&lt;MatrixType_&gt; {</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  <span class="keyword">typedef</span> MatrixXpr XprKind;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;  <span class="keyword">typedef</span> SolverStorage StorageKind;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="keyword">typedef</span> <span class="keywordtype">int</span> StorageIndex;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keyword">enum</span> { Flags = 0 };</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;};</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;}  <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html">   52</a></span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;          : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;CompleteOrthogonalDecomposition&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;{</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase&lt;CompleteOrthogonalDecomposition&gt;</a> <a class="code" href="classEigen_1_1SolverBase.html">Base</a>;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="keyword">friend</span> <span class="keyword">struct </span>internal::solve_assertion;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  EIGEN_GENERIC_PUBLIC_INTERFACE(<a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>)</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  };</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type&lt;MatrixType&gt;::type HCoeffsType;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix&lt;ColsAtCompileTime, MaxColsAtCompileTime&gt;</a></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType, Index&gt;::type</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;      IntRowVectorType;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType&gt;::type RowVectorType;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType, RealScalar&gt;::type</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;      RealRowVectorType;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequence</a>&lt;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;      MatrixType, internal::remove_all_t&lt;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                      <span class="keyword">typename</span> HCoeffsType::ConjugateReturnType&gt;&gt;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;      <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::PlainObject PlainObject;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">PermutationType::Index</a> PermIndexType;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8a94c3d01d207ef16aa2177a2b0c5953">   92</a></span>&#160;  <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8a94c3d01d207ef16aa2177a2b0c5953">CompleteOrthogonalDecomposition</a>() : m_cpqr(), m_zCoeffs(), m_temp() {}</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad8910c5d4d52bc29ecda801bd9acf10e">  100</a></span>&#160;  <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad8910c5d4d52bc29ecda801bd9acf10e">CompleteOrthogonalDecomposition</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;      : m_cpqr(rows, cols), m_zCoeffs((std::min)(rows, cols)), m_temp(cols) {}</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00120"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a94e1eb8a57d1e604b61a73a510ded439">  120</a></span>&#160;  <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a94e1eb8a57d1e604b61a73a510ded439">CompleteOrthogonalDecomposition</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;      : m_cpqr(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        m_zCoeffs((std::min)(matrix.rows(), matrix.cols())),</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        m_temp(matrix.cols())</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  {</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    compute(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  }</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00135"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae7ff6ebc9b83cbe7617b29940c4a3744">  135</a></span>&#160;  <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae7ff6ebc9b83cbe7617b29940c4a3744">CompleteOrthogonalDecomposition</a>(<a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    : m_cpqr(matrix.<a class="code" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>()),</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      m_zCoeffs((std::min)(matrix.rows(), matrix.cols())),</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;      m_temp(matrix.cols())</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  {</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">computeInPlace</a>();</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  } </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="preprocessor">  #ifdef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a6958a5faddd8f8479eb364017968833c">  154</a></span>&#160;  <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;CompleteOrthogonalDecomposition, Rhs&gt;</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a6958a5faddd8f8479eb364017968833c">solve</a>(</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;      <span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a>&amp; b) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac95b93ddad59c6e57d06fcd4737b27e1">householderQ</a>(<span class="keywordtype">void</span>) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> matrixQ(<span class="keywordtype">void</span>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a28ab9d8916ca609c5469c4c192fbfa28">householderQ</a>(); }</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a4206a90976d04c4275301b308108f60b">  163</a></span>&#160;  MatrixType <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a4206a90976d04c4275301b308108f60b">matrixZ</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    MatrixType Z = MatrixType::Identity(m_cpqr.cols(), m_cpqr.cols());</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    applyZOnTheLeftInPlace&lt;false&gt;(Z);</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keywordflow">return</span> Z;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
<div class="line"><a name="l00172"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae25bc71f3cbc01da5f63c30eed12e5c4">  172</a></span>&#160;  <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae25bc71f3cbc01da5f63c30eed12e5c4">matrixQTZ</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a484c76ad9eeae46e8a991b16fbaa14f6">matrixQR</a>(); }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
<div class="line"><a name="l00185"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">  185</a></span>&#160;  <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">matrixT</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a484c76ad9eeae46e8a991b16fbaa14f6">matrixQR</a>(); }</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&amp; compute(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix) {</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="comment">// Compute the column pivoted QR factorization A P = Q R.</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    m_cpqr.compute(matrix);</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">computeInPlace</a>();</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  }</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00196"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a284b4bb5ad267837056119f533bc7752">  196</a></span>&#160;  <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a284b4bb5ad267837056119f533bc7752">colsPermutation</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a8c0fc317edca9c71e0744dc2cd855b71">colsPermutation</a>();</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  }</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160; </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac040c34ce3fb2b68d3f57adc0c29d526">absDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160; </div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">logAbsDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">  237</a></span>&#160;  <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">rank</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a4990f19995bb873e6e33f1ec26d42c1b">rank</a>(); }</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#aa86b911cf8754fb172804966b04e6013">  246</a></span>&#160;  <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#aa86b911cf8754fb172804966b04e6013">dimensionOfKernel</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aece2257cbd8258b54759d6ed6ea9ac45">dimensionOfKernel</a>(); }</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160; </div>
<div class="line"><a name="l00255"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a381e9c1cbb5660821554fedb3d347f5d">  255</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a381e9c1cbb5660821554fedb3d347f5d">isInjective</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#afbffcdcd2b149678ee2897bf77443ab5">isInjective</a>(); }</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a52030f2aeb90d4eba8203635bf7fbec4">  264</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a52030f2aeb90d4eba8203635bf7fbec4">isSurjective</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#ac0bafd24ce9da5b1c453ec567cac36e9">isSurjective</a>(); }</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a2e1e4c484ee28a89fa821313d18691fb">  273</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a2e1e4c484ee28a89fa821313d18691fb">isInvertible</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1920097880203a64fb8493f25d8901e7">isInvertible</a>(); }</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160; </div>
<div class="line"><a name="l00280"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ab5e8b3f2c7b602772e1f1d7ce63d446e">  280</a></span>&#160;  <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Inverse.html">Inverse&lt;CompleteOrthogonalDecomposition&gt;</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ab5e8b3f2c7b602772e1f1d7ce63d446e">pseudoInverse</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;    eigen_assert(m_cpqr.m_isInitialized &amp;&amp; <span class="stringliteral">&quot;CompleteOrthogonalDecomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Inverse.html">Inverse&lt;CompleteOrthogonalDecomposition&gt;</a>(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  }</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160; </div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.rows(); }</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.cols(); }</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160; </div>
<div class="line"><a name="l00294"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#af0ede3cbb5e2878daa1a148bd3943917">  294</a></span>&#160;  <span class="keyword">inline</span> <span class="keyword">const</span> HCoeffsType&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#af0ede3cbb5e2878daa1a148bd3943917">hCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a03fede7348aadf27efbdb7af342e0619">hCoeffs</a>(); }</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160; </div>
<div class="line"><a name="l00301"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16e3f4b982e1e3506e419761a3ec96f8">  301</a></span>&#160;  <span class="keyword">const</span> HCoeffsType&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16e3f4b982e1e3506e419761a3ec96f8">zCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_zCoeffs; }</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160; </div>
<div class="line"><a name="l00322"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">  322</a></span>&#160;  <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">setThreshold</a>(<span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">threshold</a>) {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#af2983fc27ce1fe5a791fc998f9e598ce">setThreshold</a>(<a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">threshold</a>);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  }</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
<div class="line"><a name="l00335"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a416920738f4f132694b9f42029290402">  335</a></span>&#160;  <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition</a>&amp; <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a416920738f4f132694b9f42029290402">setThreshold</a>(Default_t) {</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#af2983fc27ce1fe5a791fc998f9e598ce">setThreshold</a>(Default);</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  }</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160; </div>
<div class="line"><a name="l00344"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">  344</a></span>&#160;  RealScalar <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">threshold</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a70061ce2f56d787777b9b74384ba3bc0">threshold</a>(); }</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160; </div>
<div class="line"><a name="l00353"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a1897953269e238eacea58afc3307958b">  353</a></span>&#160;  <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a1897953269e238eacea58afc3307958b">nonzeroPivots</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a161398359338bbc7daacd7e9ad4c4969">nonzeroPivots</a>(); }</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160; </div>
<div class="line"><a name="l00358"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ae90b6846f05bd30b8d52b66e427e3e09">  358</a></span>&#160;  <span class="keyword">inline</span> RealScalar <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac0e5f2123e375c181e28db748ce2b1c8">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_cpqr.<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97247d121ab174fbffcf86e6394bc2c7">maxPivot</a>(); }</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160; </div>
<div class="line"><a name="l00368"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a3521b66f1b597a2e18b13ab542cd48f4">  368</a></span>&#160;  <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a3521b66f1b597a2e18b13ab542cd48f4">info</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    eigen_assert(m_cpqr.m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  }</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160; </div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> RhsType&amp; rhs, DstType&amp; dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160; </div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  <span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  <span class="keywordtype">void</span> _solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160; </div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160; <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160; </div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;  <span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Transpose_, <span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  <span class="keywordtype">void</span> _check_solve_assertion(<span class="keyword">const</span> Rhs&amp; b)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;      EIGEN_ONLY_USED_FOR_DEBUG(b);</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;      eigen_assert(m_cpqr.m_isInitialized &amp;&amp; <span class="stringliteral">&quot;CompleteOrthogonalDecomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;      eigen_assert((Transpose_?<a class="code" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>().cols():<a class="code" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>().rows())==b.rows() &amp;&amp; <span class="stringliteral">&quot;CompleteOrthogonalDecomposition::solve(): invalid number of rows of the right hand side matrix b&quot;</span>);</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  }</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160; </div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">computeInPlace</a>();</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160; </div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;  <span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#afedd1ee41b8490b70fd1fefdd21f8c80">applyZOnTheLeftInPlace</a>(Rhs&amp; rhs) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160; </div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0a89641e0b4ea92c515405f2a31e6abe">applyZAdjointOnTheLeftInPlace</a>(Rhs&amp; rhs) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160; </div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  ColPivHouseholderQR&lt;MatrixType&gt; m_cpqr;</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  HCoeffsType m_zCoeffs;</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  RowVectorType m_temp;</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;};</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160; </div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="keyword">typename</span> MatrixType::RealScalar</div>
<div class="line"><a name="l00412"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac040c34ce3fb2b68d3f57adc0c29d526">  412</a></span>&#160;<a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac040c34ce3fb2b68d3f57adc0c29d526">CompleteOrthogonalDecomposition&lt;MatrixType&gt;::absDeterminant</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;  <span class="keywordflow">return</span> m_cpqr.absDeterminant();</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;}</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160; </div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;<span class="keyword">typename</span> MatrixType::RealScalar</div>
<div class="line"><a name="l00418"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">  418</a></span>&#160;<a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">CompleteOrthogonalDecomposition&lt;MatrixType&gt;::logAbsDeterminant</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  <span class="keywordflow">return</span> m_cpqr.logAbsDeterminant();</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;}</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00430"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">  430</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">CompleteOrthogonalDecomposition&lt;MatrixType&gt;::computeInPlace</a>()</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;{</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;  <span class="comment">// the column permutation is stored as int indices, so just to be sure:</span></div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;  eigen_assert(m_cpqr.cols() &lt;= <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;int&gt;::highest</a>());</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160; </div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rank = m_cpqr.rank();</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols = m_cpqr.cols();</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows = m_cpqr.rows();</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;  m_zCoeffs.resize((std::min)(rows, cols));</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;  m_temp.resize(cols);</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160; </div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;  <span class="keywordflow">if</span> (rank &lt; cols) {</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="comment">// We have reduced the (permuted) matrix to the form</span></div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="comment">//   [R11 R12]</span></div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    <span class="comment">//   [ 0  R22]</span></div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    <span class="comment">// where R11 is r-by-r (r = rank) upper triangular, R12 is</span></div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    <span class="comment">// r-by-(n-r), and R22 is empty or the norm of R22 is negligible.</span></div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    <span class="comment">// We now compute the complete orthogonal decomposition by applying</span></div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;    <span class="comment">// Householder transformations from the right to the upper trapezoidal</span></div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    <span class="comment">// matrix X = [R11 R12] to zero out R12 and obtain the factorization</span></div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    <span class="comment">// [R11 R12] = [T11 0] * Z, where T11 is r-by-r upper triangular and</span></div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    <span class="comment">// Z = Z(0) * Z(1) ... Z(r-1) is an n-by-n orthogonal matrix.</span></div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    <span class="comment">// We store the data representing Z in R12 and m_zCoeffs.</span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> k = rank - 1; k &gt;= 0; --k) {</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;      <span class="keywordflow">if</span> (k != rank - 1) {</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;        <span class="comment">// Given the API for Householder reflectors, it is more convenient if</span></div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;        <span class="comment">// we swap the leading parts of columns k and r-1 (zero-based) to form</span></div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;        <span class="comment">// the matrix X_k = [X(0:k, k), X(0:k, r:n)]</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;        m_cpqr.m_qr.col(k).head(k + 1).swap(</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;            m_cpqr.m_qr.col(rank - 1).head(k + 1));</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;      }</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;      <span class="comment">// Construct Householder reflector Z(k) to zero out the last row of X_k,</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;      <span class="comment">// i.e. choose Z(k) such that</span></div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;      <span class="comment">// [X(k, k), X(k, r:n)] * Z(k) = [beta, 0, .., 0].</span></div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;      RealScalar beta;</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;      m_cpqr.m_qr.row(k)</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;          .tail(cols - rank + 1)</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;          .makeHouseholderInPlace(m_zCoeffs(k), beta);</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;      m_cpqr.m_qr(k, rank - 1) = beta;</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;      <span class="keywordflow">if</span> (k &gt; 0) {</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;        <span class="comment">// Apply Z(k) to the first k rows of X_k</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;        m_cpqr.m_qr.topRightCorner(k, cols - rank + 1)</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;            .applyHouseholderOnTheRight(</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;                m_cpqr.m_qr.row(k).tail(cols - rank).adjoint(), m_zCoeffs(k),</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;                &amp;m_temp(0));</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;      }</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;      <span class="keywordflow">if</span> (k != rank - 1) {</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;        <span class="comment">// Swap X(0:k,k) back to its proper location.</span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;        m_cpqr.m_qr.col(k).head(k + 1).swap(</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;            m_cpqr.m_qr.col(rank - 1).head(k + 1));</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;      }</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    }</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;  }</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;}</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160; </div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00487"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#afedd1ee41b8490b70fd1fefdd21f8c80">  487</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#afedd1ee41b8490b70fd1fefdd21f8c80">CompleteOrthogonalDecomposition&lt;MatrixType&gt;::applyZOnTheLeftInPlace</a>(</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    Rhs&amp; rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols = this-&gt;cols();</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> nrhs = rhs.cols();</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rank = this-&gt;rank();</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;typename Rhs::Scalar, Dynamic, 1&gt;</a> temp((std::max)(cols, nrhs));</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> k = rank-1; k &gt;= 0; --k) {</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    <span class="keywordflow">if</span> (k != rank - 1) {</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;      rhs.row(k).swap(rhs.row(rank - 1));</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    }</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    rhs.middleRows(rank - 1, cols - rank + 1)</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;        .applyHouseholderOnTheLeft(</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;            matrixQTZ().row(k).tail(cols - rank).transpose().<span class="keyword">template</span> conjugateIf&lt;!Conjugate&gt;(), zCoeffs().<span class="keyword">template</span> conjugateIf&lt;Conjugate&gt;()(k),</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;            &amp;temp(0));</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;    <span class="keywordflow">if</span> (k != rank - 1) {</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;      rhs.row(k).swap(rhs.row(rank - 1));</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    }</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  }</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;}</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160; </div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00509"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0a89641e0b4ea92c515405f2a31e6abe">  509</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0a89641e0b4ea92c515405f2a31e6abe">CompleteOrthogonalDecomposition&lt;MatrixType&gt;::applyZAdjointOnTheLeftInPlace</a>(</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    Rhs&amp; rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols = this-&gt;cols();</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> nrhs = rhs.cols();</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rank = this-&gt;rank();</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;typename Rhs::Scalar, Dynamic, 1&gt;</a> temp((std::max)(cols, nrhs));</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> k = 0; k &lt; rank; ++k) {</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;    <span class="keywordflow">if</span> (k != rank - 1) {</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;      rhs.row(k).swap(rhs.row(rank - 1));</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;    }</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;    rhs.middleRows(rank - 1, cols - rank + 1)</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;        .applyHouseholderOnTheLeft(</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;            matrixQTZ().row(k).tail(cols - rank).adjoint(), zCoeffs()(k),</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;            &amp;temp(0));</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;    <span class="keywordflow">if</span> (k != rank - 1) {</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;      rhs.row(k).swap(rhs.row(rank - 1));</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;    }</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;  }</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;}</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160; </div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;<span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition&lt;MatrixType_&gt;::_solve_impl</a>(</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;    <span class="keyword">const</span> RhsType&amp; rhs, DstType&amp; dst)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rank = this-&gt;rank();</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;  <span class="keywordflow">if</span> (rank == 0) {</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;    dst.setZero();</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;  }</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160; </div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  <span class="comment">// Compute c = Q^* * rhs</span></div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  <span class="keyword">typename</span> RhsType::PlainObject c(rhs);</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;  c.applyOnTheLeft(matrixQ().setLength(rank).adjoint());</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160; </div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;  <span class="comment">// Solve T z = c(1:rank, :)</span></div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  dst.topRows(rank) = matrixT()</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;                          .topLeftCorner(rank, rank)</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;                          .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;                          .solve(c.topRows(rank));</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160; </div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols = this-&gt;cols();</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;  <span class="keywordflow">if</span> (rank &lt; cols) {</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;    <span class="comment">// Compute y = Z^* * [ z ]</span></div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;    <span class="comment">//                   [ 0 ]</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;    dst.bottomRows(cols - rank).setZero();</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;    applyZAdjointOnTheLeftInPlace(dst);</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;  }</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160; </div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;  <span class="comment">// Undo permutation to get x = P^{-1} * y.</span></div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  dst = colsPermutation() * dst;</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;}</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160; </div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;<span class="keywordtype">void</span> CompleteOrthogonalDecomposition&lt;MatrixType_&gt;::_solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rank = this-&gt;rank();</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160; </div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;  <span class="keywordflow">if</span> (rank == 0) {</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;    dst.setZero();</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;  }</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160; </div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <span class="keyword">typename</span> RhsType::PlainObject c(colsPermutation().transpose()*rhs);</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160; </div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  <span class="keywordflow">if</span> (rank &lt; cols()) {</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;    applyZOnTheLeftInPlace&lt;!Conjugate&gt;(c);</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;  }</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160; </div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;  matrixT().topLeftCorner(rank, rank)</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;           .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;           .transpose().template conjugateIf&lt;Conjugate&gt;()</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;           .solveInPlace(c.topRows(rank));</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160; </div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  dst.topRows(rank) = c.topRows(rank);</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;  dst.bottomRows(rows()-rank).setZero();</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160; </div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;  dst.applyOnTheLeft(householderQ().setLength(rank).<span class="keyword">template</span> conjugateIf&lt;!Conjugate&gt;() );</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;}</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160; </div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160; </div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;<span class="keyword">struct </span>traits&lt;Inverse&lt;CompleteOrthogonalDecomposition&lt;MatrixType&gt; &gt; &gt;</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;  : traits&lt;typename Transpose&lt;typename MatrixType::PlainObject&gt;::PlainObject&gt;</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;{</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;  <span class="keyword">enum</span> { Flags = 0 };</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;};</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160; </div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DstXprType, <span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;<span class="keyword">struct </span>Assignment&lt;DstXprType, Inverse&lt;CompleteOrthogonalDecomposition&lt;MatrixType&gt; &gt;, internal::assign_op&lt;typename DstXprType::Scalar,typename CompleteOrthogonalDecomposition&lt;MatrixType&gt;::Scalar&gt;, Dense2Dense&gt;</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;{</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  <span class="keyword">typedef</span> CompleteOrthogonalDecomposition&lt;MatrixType&gt; CodType;</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;  <span class="keyword">typedef</span> Inverse&lt;CodType&gt; SrcXprType;</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(DstXprType &amp;dst, <span class="keyword">const</span> SrcXprType &amp;src, <span class="keyword">const</span> internal::assign_op&lt;typename DstXprType::Scalar,typename CodType::Scalar&gt; &amp;)</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;  {</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;    <span class="keyword">typedef</span> Matrix&lt;typename CodType::Scalar, CodType::RowsAtCompileTime, CodType::RowsAtCompileTime, 0, CodType::MaxRowsAtCompileTime, CodType::MaxRowsAtCompileTime&gt; IdentityMatrixType;</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;    dst = src.nestedExpression().solve(IdentityMatrixType::Identity(src.cols(), src.cols()));</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;  }</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;};</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160; </div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160; </div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;<span class="keyword">typename</span> CompleteOrthogonalDecomposition&lt;MatrixType&gt;::HouseholderSequenceType</div>
<div class="line"><a name="l00617"></a><span class="lineno"><a class="line" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac95b93ddad59c6e57d06fcd4737b27e1">  617</a></span>&#160;<a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac95b93ddad59c6e57d06fcd4737b27e1">CompleteOrthogonalDecomposition&lt;MatrixType&gt;::householderQ</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  <span class="keywordflow">return</span> m_cpqr.householderQ();</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;}</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160; </div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;<span class="keyword">const</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>&gt;</div>
<div class="line"><a name="l00627"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ae90b6846f05bd30b8d52b66e427e3e09">  627</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#ae90b6846f05bd30b8d52b66e427e3e09">MatrixBase&lt;Derived&gt;::completeOrthogonalDecomposition</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1CompleteOrthogonalDecomposition.html">CompleteOrthogonalDecomposition&lt;PlainObject&gt;</a>(eval());</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;}</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160; </div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160; </div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H</span></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a03fede7348aadf27efbdb7af342e0619"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a03fede7348aadf27efbdb7af342e0619">Eigen::ColPivHouseholderQR::hCoeffs</a></div><div class="ttdeci">const HCoeffsType &amp; hCoeffs() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:336</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a161398359338bbc7daacd7e9ad4c4969"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a161398359338bbc7daacd7e9ad4c4969">Eigen::ColPivHouseholderQR::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:396</div></div>
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<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a28ab9d8916ca609c5469c4c192fbfa28"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a28ab9d8916ca609c5469c4c192fbfa28">Eigen::ColPivHouseholderQR::householderQ</a></div><div class="ttdeci">HouseholderSequenceType householderQ() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:652</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a484c76ad9eeae46e8a991b16fbaa14f6"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a484c76ad9eeae46e8a991b16fbaa14f6">Eigen::ColPivHouseholderQR::matrixQR</a></div><div class="ttdeci">const MatrixType &amp; matrixQR() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:191</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a4990f19995bb873e6e33f1ec26d42c1b"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a4990f19995bb873e6e33f1ec26d42c1b">Eigen::ColPivHouseholderQR::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:257</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a70061ce2f56d787777b9b74384ba3bc0"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a70061ce2f56d787777b9b74384ba3bc0">Eigen::ColPivHouseholderQR::threshold</a></div><div class="ttdeci">RealScalar threshold() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:380</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a8c0fc317edca9c71e0744dc2cd855b71"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a8c0fc317edca9c71e0744dc2cd855b71">Eigen::ColPivHouseholderQR::colsPermutation</a></div><div class="ttdeci">const PermutationType &amp; colsPermutation() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:216</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_a97247d121ab174fbffcf86e6394bc2c7"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a97247d121ab174fbffcf86e6394bc2c7">Eigen::ColPivHouseholderQR::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:405</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_ac0bafd24ce9da5b1c453ec567cac36e9"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#ac0bafd24ce9da5b1c453ec567cac36e9">Eigen::ColPivHouseholderQR::isSurjective</a></div><div class="ttdeci">bool isSurjective() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:300</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_aece2257cbd8258b54759d6ed6ea9ac45"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#aece2257cbd8258b54759d6ed6ea9ac45">Eigen::ColPivHouseholderQR::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:274</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_af2983fc27ce1fe5a791fc998f9e598ce"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#af2983fc27ce1fe5a791fc998f9e598ce">Eigen::ColPivHouseholderQR::setThreshold</a></div><div class="ttdeci">ColPivHouseholderQR &amp; setThreshold(const RealScalar &amp;threshold)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:355</div></div>
<div class="ttc" id="aclassEigen_1_1ColPivHouseholderQR_html_afbffcdcd2b149678ee2897bf77443ab5"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#afbffcdcd2b149678ee2897bf77443ab5">Eigen::ColPivHouseholderQR::isInjective</a></div><div class="ttdeci">bool isInjective() const</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:287</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html">Eigen::CompleteOrthogonalDecomposition</a></div><div class="ttdoc">Complete orthogonal decomposition (COD) of a matrix.</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:54</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a0a89641e0b4ea92c515405f2a31e6abe"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0a89641e0b4ea92c515405f2a31e6abe">Eigen::CompleteOrthogonalDecomposition::applyZAdjointOnTheLeftInPlace</a></div><div class="ttdeci">void applyZAdjointOnTheLeftInPlace(Rhs &amp;rhs) const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:509</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a0ea6a40374c16331f8d323d1f64bf57e"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a0ea6a40374c16331f8d323d1f64bf57e">Eigen::CompleteOrthogonalDecomposition::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:237</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a16c1fd97a7ef99d1cf64f8cf1ee81cbf"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a16c1fd97a7ef99d1cf64f8cf1ee81cbf">Eigen::CompleteOrthogonalDecomposition::threshold</a></div><div class="ttdeci">RealScalar threshold() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:344</div></div>
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<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a2e1e4c484ee28a89fa821313d18691fb"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a2e1e4c484ee28a89fa821313d18691fb">Eigen::CompleteOrthogonalDecomposition::isInvertible</a></div><div class="ttdeci">bool isInvertible() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:273</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a3521b66f1b597a2e18b13ab542cd48f4"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a3521b66f1b597a2e18b13ab542cd48f4">Eigen::CompleteOrthogonalDecomposition::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdoc">Reports whether the complete orthogonal decomposition was successful.</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:368</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a381e9c1cbb5660821554fedb3d347f5d"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a381e9c1cbb5660821554fedb3d347f5d">Eigen::CompleteOrthogonalDecomposition::isInjective</a></div><div class="ttdeci">bool isInjective() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:255</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a416920738f4f132694b9f42029290402"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a416920738f4f132694b9f42029290402">Eigen::CompleteOrthogonalDecomposition::setThreshold</a></div><div class="ttdeci">CompleteOrthogonalDecomposition &amp; setThreshold(Default_t)</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:335</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a4206a90976d04c4275301b308108f60b"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a4206a90976d04c4275301b308108f60b">Eigen::CompleteOrthogonalDecomposition::matrixZ</a></div><div class="ttdeci">MatrixType matrixZ() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:163</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a52030f2aeb90d4eba8203635bf7fbec4"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a52030f2aeb90d4eba8203635bf7fbec4">Eigen::CompleteOrthogonalDecomposition::isSurjective</a></div><div class="ttdeci">bool isSurjective() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:264</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a6958a5faddd8f8479eb364017968833c"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a6958a5faddd8f8479eb364017968833c">Eigen::CompleteOrthogonalDecomposition::solve</a></div><div class="ttdeci">const Solve&lt; CompleteOrthogonalDecomposition, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a8a94c3d01d207ef16aa2177a2b0c5953"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8a94c3d01d207ef16aa2177a2b0c5953">Eigen::CompleteOrthogonalDecomposition::CompleteOrthogonalDecomposition</a></div><div class="ttdeci">CompleteOrthogonalDecomposition()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:92</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a8f0580429cdba56ea1fd7ae5f8d48774"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8f0580429cdba56ea1fd7ae5f8d48774">Eigen::CompleteOrthogonalDecomposition::matrixT</a></div><div class="ttdeci">const MatrixType &amp; matrixT() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:185</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a8fa642ffb4181e550a593d71fc0d03bf"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a8fa642ffb4181e550a593d71fc0d03bf">Eigen::CompleteOrthogonalDecomposition::setThreshold</a></div><div class="ttdeci">CompleteOrthogonalDecomposition &amp; setThreshold(const RealScalar &amp;threshold)</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:322</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_a94e1eb8a57d1e604b61a73a510ded439"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#a94e1eb8a57d1e604b61a73a510ded439">Eigen::CompleteOrthogonalDecomposition::CompleteOrthogonalDecomposition</a></div><div class="ttdeci">CompleteOrthogonalDecomposition(const EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructs a complete orthogonal decomposition from a given matrix.</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:120</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_aa86b911cf8754fb172804966b04e6013"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#aa86b911cf8754fb172804966b04e6013">Eigen::CompleteOrthogonalDecomposition::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:246</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ab5e8b3f2c7b602772e1f1d7ce63d446e"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ab5e8b3f2c7b602772e1f1d7ce63d446e">Eigen::CompleteOrthogonalDecomposition::pseudoInverse</a></div><div class="ttdeci">const Inverse&lt; CompleteOrthogonalDecomposition &gt; pseudoInverse() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:280</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ac040c34ce3fb2b68d3f57adc0c29d526"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac040c34ce3fb2b68d3f57adc0c29d526">Eigen::CompleteOrthogonalDecomposition::absDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar absDeterminant() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:412</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ac0e5f2123e375c181e28db748ce2b1c8"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac0e5f2123e375c181e28db748ce2b1c8">Eigen::CompleteOrthogonalDecomposition::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:358</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ac95b93ddad59c6e57d06fcd4737b27e1"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ac95b93ddad59c6e57d06fcd4737b27e1">Eigen::CompleteOrthogonalDecomposition::householderQ</a></div><div class="ttdeci">HouseholderSequenceType householderQ(void) const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:617</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ad59d6dc78dab52a0038ac372b4a72c0d"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad59d6dc78dab52a0038ac372b4a72c0d">Eigen::CompleteOrthogonalDecomposition::logAbsDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar logAbsDeterminant() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:418</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ad8910c5d4d52bc29ecda801bd9acf10e"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ad8910c5d4d52bc29ecda801bd9acf10e">Eigen::CompleteOrthogonalDecomposition::CompleteOrthogonalDecomposition</a></div><div class="ttdeci">CompleteOrthogonalDecomposition(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:100</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_adb0b963d7d8f96492904e8eda03efbf5"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#adb0b963d7d8f96492904e8eda03efbf5">Eigen::CompleteOrthogonalDecomposition::computeInPlace</a></div><div class="ttdeci">void computeInPlace()</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:430</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ae25bc71f3cbc01da5f63c30eed12e5c4"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae25bc71f3cbc01da5f63c30eed12e5c4">Eigen::CompleteOrthogonalDecomposition::matrixQTZ</a></div><div class="ttdeci">const MatrixType &amp; matrixQTZ() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:172</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_ae7ff6ebc9b83cbe7617b29940c4a3744"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#ae7ff6ebc9b83cbe7617b29940c4a3744">Eigen::CompleteOrthogonalDecomposition::CompleteOrthogonalDecomposition</a></div><div class="ttdeci">CompleteOrthogonalDecomposition(EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructs a complete orthogonal decomposition from a given matrix.</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:135</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_af0ede3cbb5e2878daa1a148bd3943917"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#af0ede3cbb5e2878daa1a148bd3943917">Eigen::CompleteOrthogonalDecomposition::hCoeffs</a></div><div class="ttdeci">const HCoeffsType &amp; hCoeffs() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:294</div></div>
<div class="ttc" id="aclassEigen_1_1CompleteOrthogonalDecomposition_html_afedd1ee41b8490b70fd1fefdd21f8c80"><div class="ttname"><a href="classEigen_1_1CompleteOrthogonalDecomposition.html#afedd1ee41b8490b70fd1fefdd21f8c80">Eigen::CompleteOrthogonalDecomposition::applyZOnTheLeftInPlace</a></div><div class="ttdeci">void applyZOnTheLeftInPlace(Rhs &amp;rhs) const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:487</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderSequence_html"><div class="ttname"><a href="classEigen_1_1HouseholderSequence.html">Eigen::HouseholderSequence</a></div><div class="ttdoc">Sequence of Householder reflections acting on subspaces with decreasing size.</div><div class="ttdef"><b>Definition:</b> HouseholderSequence.h:123</div></div>
<div class="ttc" id="aclassEigen_1_1Inverse_html"><div class="ttname"><a href="classEigen_1_1Inverse.html">Eigen::Inverse</a></div><div class="ttdoc">Expression of the inverse of another expression.</div><div class="ttdef"><b>Definition:</b> Inverse.h:46</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_ae90b6846f05bd30b8d52b66e427e3e09"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#ae90b6846f05bd30b8d52b66e427e3e09">Eigen::MatrixBase::completeOrthogonalDecomposition</a></div><div class="ttdeci">const CompleteOrthogonalDecomposition&lt; PlainObject &gt; completeOrthogonalDecomposition() const</div><div class="ttdef"><b>Definition:</b> CompleteOrthogonalDecomposition.h:627</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix&lt; ColsAtCompileTime, MaxColsAtCompileTime &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1Solve_html"><div class="ttname"><a href="classEigen_1_1Solve.html">Eigen::Solve</a></div><div class="ttdoc">Pseudo expression representing a solving operation.</div><div class="ttdef"><b>Definition:</b> Solve.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html"><div class="ttname"><a href="classEigen_1_1SolverBase.html">Eigen::SolverBase</a></div><div class="ttdoc">A base class for matrix decomposition and solvers.</div><div class="ttdef"><b>Definition:</b> SolverBase.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::SolverBase&lt; CompleteOrthogonalDecomposition&lt; MatrixType_ &gt; &gt;::derived</a></div><div class="ttdeci">CompleteOrthogonalDecomposition&lt; MatrixType_ &gt; &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition:</b> EigenBase.h:41</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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